Chapter 13.3, Problem 21WE

To determine

To find: The sum has a period that divides $p$ .

Answer to Problem 21WE

The period of $f\left(x\right)+g\left(x\right)=\sin x+\sin 2xis2\pi$ .

Explanation of Solution

Given information:

The given function is $h\left(x\right)=f\left(x\right)+g\left(x\right)$

Calculation:

Calculate the function is

Let $f\left(x\right)=\sin xandg\left(x\right)=\sin 2x$

Amplitude

Period $=\left[\frac{2\pi }{B}\right]$

For $f\left(x\right)=\sin x$

Period $\begin{array}{l}=\left[\frac{2\pi }{1}\right]\\ =2\pi \end{array}$

Again for $g\left(x\right)=\sin 2x$

Period $\left[\frac{2\pi }{2}\right]=\pi$

Therefore the period of $f\left(x\right)+g\left(x\right)=\sin x+\sin 2xis2\pi$